SISSA Springer Series
Volume 1 / 2019 to Volume 5 / 2024
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Article
A finite element implementation of finite deformation surface and bulk poroelasticity
We present a theoretical and computational model for the behavior of a porous solid undergoing two interdependent processes, the finite deformation of a solid and species migration through the solid, which are...
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Article
Reduced Order Modeling for Real-Time Stent Deformation Simulations of Transcatheter Aortic Valve Prostheses
Computational modeling can be a critical tool to predict deployment behavior for transcatheter aortic valve replacement (TAVR) in patients with aortic stenosis. However, due to the mechanical complexity of the...
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Book Series
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Chapter
Worked Out Problem 9: A Thermal Conduction Problem Through an Extended Surface
In this chapter, we consider a scalar elliptic PDE modeling the steady-state heat transfer problem through a two-dimensional geometrically parametrized fin. The aim is to obtain efficient evaluations of the th...
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Chapter
Worked Out Problem 11: A Linear Elasticity Application on a Beam Bridge
In this chapter, we consider a vector elliptic PDE modeling a linear elasticity problem for bridge designing in a two-dimensional and geometrically parametrized domain. The aim is to obtain efficient evaluatio...
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Chapter
Worked Out Problem 13: Bifurcating Coanda Effect in a Channel
In this chapter, we consider a vector steady nonlinear PDE modeling the bifurcating Coanda effect for an incompressible flow in a two-dimensional channel. The aim is to obtain efficient evaluations of the velo...
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Chapter
Worked Out Problem 2: A Linear Elasticity Problem on a Square
In this chapter, we consider a vector elliptic PDE modeling a parametric linear elasticity problem in a two-dimensional heterogeneous domain. The aim is to obtain efficient evaluations of the vector displaceme...
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Chapter
Worked Out Problem 15: Stabilized Reduced Method for an Advection Dominated Problem
In this chapter, we consider a scalar advection-diffusion PDE modeling a stabilized advection dominated flow problem in a two-dimensional domain. The aim is to obtain efficient evaluations of the unknown field...
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Chapter
Worked Out Problem 4: A Transport Problem for the 2D Graetz Flow
In this chapter, we consider a scalar advection-diffusion PDE modeling the Graetz flow problem in a two-dimensional and geometrically parametrized domain. The aim is to obtain efficient evaluations of the ther...
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Chapter
Worked Out Problem 17: Uncertainty Quantification for a Stochastic Thermal Block
In this chapter, we consider a vector elliptic stochastic PDE modeling a steady heat conduction in a two-dimensional heterogeneous domain based on random input data. The aim is to obtain efficient evaluation o...
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Chapter
Worked Out Problem 6: Unsteady Heat Conduction in a Thermal Block
In this chapter, we consider a parabolic PDE modeling the unsteady conduction problem in a two-dimensional domain. The aim is to obtain efficient evaluations of the time evolution of the thermal field and the ...
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Chapter
Worked Out Problem 8: A Nonlinear Parabolic FitzHugh–Nagumo Problem
In this chapter, we consider a vector nonlinear parabolic PDE modeling the unsteady FitzHugh–Nagumo system in a one-dimensional domain. The aim is to obtain efficient evaluations of the unknown fields describi...
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Chapter
Worked Out Problem 10: An Idealized Contact Problem in Linear Elasticity with Friction
In this chapter, we consider a vector elliptic PDE modeling a contact problem in linear elasticity with friction in a two-dimensional and geometrically parametrized domain. The aim is to obtain efficient evalu...
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Chapter
Worked Out Problem 12: Navier-Stokes System for a Backward-Facing Step
In this chapter, we consider a vector steady nonlinear PDE modeling the Navier–Stokes system for an incompressible flow in a two-dimensional domain. The aim is to obtain efficient evaluations of the velocity a...
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Chapter
Worked Out Problem 1: Steady Heat Conduction in a Thermal Block
In this chapter, we consider a scalar elliptic PDE modeling a parametric steady heat conduction problem in a two-dimensional domain. The aim is to obtain efficient evaluations of the thermal field and the outp...
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Chapter
Worked Out Problem 14: Unsteady Navier-Stokes Equations for Vortex Shedding Behind a Cylinder
In this chapter, we consider a vector time-dependent nonlinear PDE modeling the unsteady Navier-Stokes system for an incompressible flow in a two-dimensional domain with a cylindrical obstacle. The aim is to o...
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Chapter
Worked Out Problem 3: Thermal Transfer Problem in a Parametrized Geometry
In this chapter, we consider a scalar elliptic PDE modeling a steady-state heat conduction problem in a two-dimensional and geometrically parametrized holed domain. The aim is to obtain efficient evaluations o...
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Chapter
Worked Out Problem 16: A Parametrized Elliptic Optimal Control Problem
In this chapter, we consider a linear-quadratic optimal control problem with a vector elliptic PDE constraint in a two-dimensional and geometrically parametrized domain. The aim is to obtain efficient evaluati...
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Chapter
Worked Out Problem 5: Heat Conduction with Gaussian Flux
In this chapter, we consider a scalar elliptic PDE modeling the steady heat conduction problem with a non-affine Gaussian flux in a two-dimensional domain. The aim is to obtain efficient evaluations of the the...
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Chapter
Worked Out Problem 7: A Nonlinear Elliptic Problem
In this chapter, we consider a scalar nonlinear elliptic PDE as a benchmark for complex material problems in a two-dimensional domain. The aim is to obtain efficient evaluations of the unknown field and the ou...
